How far is it from Lebanon to Israel?

The two countries share a border, along Israel's north / Lebanon's south.

Along that line, the distance between them is zero.

In terms of getting from Lebanon to Israel, you would need to travel through Syria and Jordan before crossing the Israeli-Jordanian border. This trip is roughly 60 miles or 100 kilometers. There are two things worth noting about this travel.

1. This can only be done from Lebanon to Israel (as opposed to from Israel to Lebanon) since Israel will accept someone with a Lebanese and Syrian passport stamp (unhappily, but they will) whereas Lebanon and Syria explicitly ban Israeli-stamped passports.
2. Syria is currently in a state of civil war, so it is not a smart idea to drive through Syria.